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A Sequent Formulation of Conditional Logic Based on Belief Change Operations

Peter Roeper
Studia Logica: An International Journal for Symbolic Logic
Vol. 77, No. 3 (Aug., 2004), pp. 425-438
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016637
Page Count: 14
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A Sequent Formulation of Conditional Logic Based on Belief Change Operations
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Abstract

Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of $\text{information}^{1}$. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truth-functional part of the logic as given, the present paper proposes a semantics entirely based on epistemic states and operations on these states. The semantics is accompanied by a syntactic treatment of conditional logic which is formally similar to Gentzen's sequent formulation of natural deduction $\text{rules}^{2}$. Three of David Lewis's systems of conditional logic are represented. The formulations are attractive by virtue of their transparency and simplicity.

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